Abstract. Let w be an equality word of two nonperiodic binary morphisms g, h : {a, b} . Suppose that no overflow occurs twice in w and that w contains at least 9 occurrences of a and at least 9 occurrences of b. Then either w = (ab)i a, or w = ai bj with gcd(i, j) = 1, up to the exchange of letters a and b.